Question

What is the factored form of 64g^3+8?

(4G+2)(16g^2+8g-4
(4g+2)(16g^2-8g-4
(4g+2)(16g^2+8g+4
(4g+2)(16g^2-8g+4

Answer 1

Answer:

8 (2 g + 1) (4 g^2 - 2 g + 1)

Step-by-step explanation:

Factor the following:

64 g^3 + 8

Factor 8 out of 64 g^3 + 8:

8 (8 g^3 + 1)

8 g^3 + 1 = (2 g)^3 + 1^3:

8 (2 g)^3 + 1^3

Factor the sum of two cubes. (2 g)^3 + 1^3 = (2 g + 1) ((2 g)^2 - 2 g + 1^2):

8 (2 g + 1) ((2 g)^2 - 2 g + 1^2)

1^2 = 1:

8 (2 g + 1) ((2 g)^2 - 2 g + 1)

Multiply each exponent in 2 g by 2:

8 (2 g + 1) (4 g^2 - 2 g + 1)

2^2 = 4:

Answer: 8 (2 g + 1) (4 g^2 - 2 g + 1)

Answer 2

Answer:

(4g+2)(16^2-8g+4)

Step-by-step explanation:

Method 1

Since you've been given possible answers,expand each option. The option which gives 64g^3+8 is the answer.

Method 2

use the formula (a+b) (a^2-ab+b^2)

where a is 64g^3

b is 8

find the cubic root of a and b

a=4g

b=2

substituting a and b into the formula

(4g+2)(4g)^2-2.(4g)+2^2)

(4g+2) (16g^2-8g+4)